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QUESTION 9. Convert the following CFG to a CFG in Chomsky Normal Form (CNF): G=(V, {0, 1), P, S), where V = {S, A, B, C, D) and P contains the following rules: S→ AB|AC|D A → 0A0|1A1|0 B→ OB|1B|e D→ AA

QUESTION 9. Convert the following CFG to a CFG in Chomsky Normal Form (CNF): G=(V, {0, 1), P, S), where V = {S, A, B, C, D) and P contains the following rules: S→ AB|AC|D A → 0A0|1A1|0 B→ OB|1B|e D→ AA

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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### Conversion of CFG to Chomsky Normal Form (CNF) #### Question 9: Convert the following CFG to a CFG in Chomsky Normal Form (CNF) Given \( G = (V, \{0, 1\}, P, S) \), where \( V = \{S, A, B, C, D\} \) and \( P \) contains the following rules: - \( S \rightarrow AB | AC | D \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | \epsilon | 1 \) - \( D \rightarrow AA \) #### 1. Elimination of \( \epsilon \)-productions: - \( S \rightarrow AB | AC | D | A \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) - \( D \rightarrow AA \) #### 2. Elimination of unit-productions: - \( S \rightarrow AB | AC | 1A | 0A | 0A0 | 1A1 | 0 \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) - \( D \rightarrow AA \) #### 3. Elimination of useless variables: - \( C \) is eliminated because it is not generating. - \( D \) is eliminated because it is not reachable. Resulting in: - \( S \rightarrow AB | A0 | A | A1 | 0 \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) #### 4. Final Answer: - \( S \rightarrow AB | AA0 | AO | A1 | 0 \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) - \( A_0 \rightarrow AO \) - \( A_1 \rightarrow A1 \) - \( O \rightarrow
Transcribed Image Text:### Conversion of CFG to Chomsky Normal Form (CNF) #### Question 9: Convert the following CFG to a CFG in Chomsky Normal Form (CNF) Given \( G = (V, \{0, 1\}, P, S) \), where \( V = \{S, A, B, C, D\} \) and \( P \) contains the following rules: - \( S \rightarrow AB | AC | D \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | \epsilon | 1 \) - \( D \rightarrow AA \) #### 1. Elimination of \( \epsilon \)-productions: - \( S \rightarrow AB | AC | D | A \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) - \( D \rightarrow AA \) #### 2. Elimination of unit-productions: - \( S \rightarrow AB | AC | 1A | 0A | 0A0 | 1A1 | 0 \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) - \( D \rightarrow AA \) #### 3. Elimination of useless variables: - \( C \) is eliminated because it is not generating. - \( D \) is eliminated because it is not reachable. Resulting in: - \( S \rightarrow AB | A0 | A | A1 | 0 \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) #### 4. Final Answer: - \( S \rightarrow AB | AA0 | AO | A1 | 0 \) - \( A \rightarrow 0A0 | 1A1 | 0 \) - \( B \rightarrow 0B | 1B | 0 | 1 \) - \( A_0 \rightarrow AO \) - \( A_1 \rightarrow A1 \) - \( O \rightarrow
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